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Option (a) 3²⁰⁰ = (3²)¹⁰⁰ = 9¹⁰⁰
Option (c) 4¹⁰⁰
Option (d) 2³⁰⁰ = (2³)¹⁰⁰ = 8¹⁰⁰
Clearly, among the option (a), (c) and (d) the exponent is same.
So, the option with largest base will be largest.
So, among these three options, option (a) is largest.
Now option (b) is 2¹⁰⁰ + 3¹⁰⁰ < 3¹⁰⁰ + 3¹⁰⁰
Or, 2¹⁰⁰ + 3¹⁰⁰ < 2x 3¹⁰⁰
And, 2x3¹⁰⁰ is certainly less than 3²⁰⁰ i.e. option (a)
That means, option (b) is less than option (a).
∴ Option (a) is the highest.